The **hypotenuse** is the side that is opposite of the right angle or the longest side of the right triangle. The other two sides are called the opposite and adjacent sides. This is a step-by-step guide that will teach you how to find a hypotenuse when you know the other two sides of the right triangle and also when you know an angle and side.

**Right Triangle:** If a triangle contains one angle that is exactly 90 degrees then it is a right triangle.**Trigonometric Ratios: **

**S**ine: sin(θ) =

**O**pposite /

**H**ypotenuse

**C**osine: cos(θ) =

**A**djacent /

**H**ypotenuse

**T**angent: tan(θ) = Opposite / Adjacent

**Sides of an Angle: **

– Adjacent is next to the angle.

– Opposite is opposite to the angle.

– The longest side is the hypotenuse

Contents

## How to Find Hypotenuse when we know the Sides

- Make sure the
**triangle is a right triangle**. - Recall the
**Pythagorean Theorem. (**)**a**^{2}+ b^{2}=c^{2} **Look at the triangle**and identify the values for a, b and c.**Plugin the values of legs(a&b)**into the Pythagorean Theorem.**Solve the equation**to get the value of c.

For Example,

## How to Find Hypotenuse when we know a Side and an Angle

- Understand the
**sides of an angle**. - Recall the
**trigonometric ratios**. - Apply the
**Sine trigonometric relationship**to find the hypotenuse. **Solve the equation**to get the value of Hypotenuse.

For Example,